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					Banking                                                                                       273




                                            12

                                       Banking


12.1 INTRODUCTION
All of us need money to meet our day-to-day expenses. We earn money, spend money and also,
save some money. We would like to keep the money in safe custody. Banks are the institutions
where we keep the money in the form of deposits and those who need money can borrow as
loans on payment of interest with certain conditions. Besides this, banks also help the people
in various kinds of financial transactions. Some of the functions of a bank are :

  1. Keeping money of the depositors and pay interest on deposits.

  2. Giving loans to the borrowers on interest.

  3. Buying and selling security bonds.

  4. Receiving payments – Telephone bills, Electricity bills, water bills, school fees etc.

  5. Transferring money from one place to another.

  6. Collection of taxes – income tax, sales tax, house tax etc.

  7. Issuing/Encashing travellers cheques in Local/Foreign currency.

  8. Providing All Time Money (ATM) facility to the customers.

  9. Issuing credit cards.

 10. Exchange of Foreign currency etc.

For the convenience of customers, the banks offer different types of accounts (deposits) some
of which are :

 (i) Savings Bank Account

 (ii) Current Account

(iii) Fixed deposit Account.

(iv) Recurring deposit Account.
274                                                                                    Mathematics


12.2 OBJECTIVES
After studying this lesson, the learner will be able to :

      state different types of accounts.

      calculate interest for a saving bank account, given the rate of interest.

      calculate interest/maturity value of fixed/term deposit given the rate of interest compounded
      yearly, semi-annually or quarterly (not more than four conversion periods).

12.3 EXPECTED BACKGROUND KNOWLEDGE
 (i) Knowledge of simple interest when principal (P), rate of interest (R) and time (T), for
     which money was invested are given i.e. S.I. = PRT.

 (ii) Compound interest when P, R, n are given i.e., C.I. = A – P where

                           A = P(1 + R)n, n is number of conversion periods.

12.4 TYPES OF ACCOUNTS
You can open different types of accounts in a bank depending upon your needs. Some of these
are :
 (a) Savings bank account
 (b) Fixed or term deposit account
 (c) Current account

12.4.1 Savings Bank Account
This is the most popular account offered by the banks. This account encourages people to
develop the habit of saving. Anybody can open this account with a minimum sum of Rs 1000
with cheque book facility. In this account, deposits and withdrawals can be made and the record
is maintained by the bank in a ‘Pass-Book’ given to the Account holder (i.e. the person who
holds the account).

The bank pays interest for the money that an account holder keeps in the account. The prevailing
rate of interest is 4% per annum compounded half yearly. The rate of interest changes from
time to time.

On opening a savings bank account, a pass book is issued to the account holder. It contains
date wise entries of deposits withdrawals and the interest earned. It bears savings bank account
number also.

The general format of a page of the savings bank passbook is as given below :
Banking                                                                                  275



 Date          Particulars       Amount withdrawn         Amount Deposited        Balance
                                  Rs          P            Rs         P
 —                 —                       —                         —               —
 —                 —                       —                         —               —
 —                 —                       —                         —               —

Money can be withdrawn from the bank through a withdrawal slip (sample shown) or by a
cheque (sample shown below).




                               Fi.g 12.1 Sample of Withdrawal slip




                                  Fig. 12.2 Sample of Cheque

Note : In a savings bank account,
 (i) The bank pays interest for the month on the minimum closing balance from the 10th day
     of the month to the last day of the month.
 (ii) The interest is credited to the account every six months.
(iii) The present rate of interest is 4% per annum compounded semi-annually.
(iv) Usually not more than 25 withdrawals are allowed in a quarter from Savings Bank account.
276                                                                               Mathematics


12.4.2 Computation of Interest
 (i) Write down the minimum balance between the closing balance on 10th to the last day
     of the month.
 (ii) Add all the minimum balances for each month as per step (i) to obtain principal for one
      month.
(iii) Calculate the simple interest on this sum for one month using the formula

                                           1
                     Interest = P × R ×
                                          12

      where P is Principal, R is rate of interest per annum and time 1 month i.e. 1/12 year.
(iv) If account is opened after the 10th day of month, no interest is payable for that month.
 (v) No interest is paid for the month in which the account is closed.
Let us illustrate the above with some examples.
Example 12.1 : Sidharth opened a savings bank account in State Bank of India on 5th
March 2003 with a deposit of Rs 5000. He deposited Rs 1500 on 10th March 2003 and withdrew
Rs 3000 on 29th March, 2003. Find the principal for which he will earn interest for
March 2003.
Solution : Balance on 5th March, 2003 = Rs 5000
Balance on 10th March, 2003 = Rs 6500
Balance on 29th March, 2003 = Rs 3500
Here minimum balance between 10th and 31st March, 2003 = Rs 3500.
Therefore, the principal for which interest is earned for the month of March 2003 is Rs 3500.
Example 12.2 : Anisha’s savings bank account pass-book has the following entries :
          Date        Particulars   Amount withdrawn Amount Deposited Balance
                                      Rs         P     Rs       P     Rs P
          2002
          Jan 6       By Cash                    —          20000.00        20000.00
          Feb 11      By Cash                    —          10000.00        30000.00
          April 5     By Cheque                  —           5000.00        35000.00
          April 27    To Cheque                18000.00         —           17000.00
          May 3       By Cash                    —          13000.00        30000.00
          June 15     To Cheque                20000.00         —           10000.00

Find the sum on which Anisha will earn interest from January to June 2002.
Banking                                                                                    277


Solution : The qualifying amount for the interest is the minimum balance between the 10th
and the last day of the month.
                 Principal for January    = Rs        20000
                 Principal for February = Rs          20000
                 Principal for March      = Rs        30000
                 Principal for April      = Rs        17000
                 Principal for May        = Rs        30000
                 Principal for June       = Rs        10000
                 Total                       Rs 127000
Thus, the sum on which Anisha will earn interest for one month = Rs 127000.
Example 12.3 : Ritus’s pass book has the following entries :

          Date            Particulars   Amount withdrawn Amount Deposited Balance
                                          Rs        P      Rs       P     Rs P
          2002
          Jan. 1         B/F                  —                      —        12000.00
          Jan. 9         To Cash           Rs 7000.00                —        5000.00
          Jan. 11        By Cheque            —                    20000.00   25000.00
          Feb. 10        To Cheque        Rs 10000.00                —        15000.00
          April 3        By Cash              —                    5000.00    20000.00
          June 5         By Cheque            —                    10000.00   30000.00
          June 25        By Cheque            —                    5000.00    35000.00

If the rate of interest is 4% per annum, find the interest earned by Ritu at the end of June on
her savings bank account.
Solution : Details of qualifying amount for the calculation of interest are as below:
                          Month                        Amount
                          Jan.                   Rs      5000.00
                          Feb.                   Rs     15000.00
                          March                  Rs     15000.00
                          April                  Rs     20000.00
                          May                    Rs     20000.00
                          June                   Rs     30000.00
                          Total                  Rs    105000.00
278                                                                                 Mathematics


                                                  1
Here P = Rs 105000, R = 4% and T =                  year.
                                                 12

                                          105000 × 4 × 1
           ∴           Interest = PRT = Rs               = Rs 350.
                                            100 × 12
           ∴     Interest earned by Ritu = Rs 350.
Example 12.4 : Ashok has a savings bank account in a bank. His passbook has the following
entries:
      Date             Particulars    Amount withdrawn Amount Deposited Balance
                                        Rs        P      Rs       P     Rs P
      2002
      July 11      By cash                        —              6000.00        6000.00
      Aug 12       By Cheque                      —              4000.00       10000.00
      Sept 5       By Cheque                      —             10000.00       20000.00
      Sept 21      To Cheque                 8000.00                 —         12000.00
      Nov 9        By Cheque                      —              8000.00       20000.00
      Dec 10       By Cheque                      —             10000.00       30000.00
      Dec 29       To cash                  26000.00                 —          4000.00

The account is closed on 3rd January 2003. Find the amount received by Ashok, if the rate
of interest is 4% per annum.
Solution. Details of qualifying amount for the calculation of interest are :
                Month                            Amount
                July                      Rs               —
                August                    Rs       6000.00
                September                 Rs      12000.00
                October                   Rs      12000.00
                November                  Rs      20000.00
                December                  Rs       4000.00
                Total                     Rs      54000.00

                                                  1
Here P = Rs 54000, R = 4% and T =                   year
                                                 12

                            LM 54000 × 4 × 1OP
∴ Interest = PRT = Rs
                             N 100 × 12 Q         = Rs 180.00

∴ Amount received = Rs (4000 + 180) = Rs 4180.
Banking                                                                                  279


Example 12.5 : The dates and respective balances in the pass book of David’s savings bank
account are given below :

                  Dates                          Balances
                  2002
                  October 5                 Rs      1500.00
                  October 25                Rs      3500.00
                  December 8                Rs      5000.00
                  2003
                  January 11                Rs      8000.00
                  February 5                Rs      6000.00
                  February 9                Rs     10000.00
                  February 11               Rs      7500.00
                  March 15                  Rs     20000.00
                  March 29                  Rs     10000.00

Calculate the interest earned upto March 2003 if the rate of interest is 4% per annum.
Solution : Details of qualifying amount for the calculation of interest are :
                  Month                      Amount
                  Oct, 2002                 Rs     1500
                  Nov, 2002                 Rs     3500
                  Dec, 2002                 Rs     5000
                  Jan, 2003                 Rs     5000
                  Feb, 2003                 Rs     7500
                  March 2003                Rs     7500
                  Total                     Rs 30000

Here P = Rs 30000, R = 4%            and T = 1/12 year

                          30000 × 4 × 1
∴ Interest = PRT = Rs                   = Rs 100
                            100 × 12

∴ Interest earned by David = Rs 100.
280                                                                                               Mathematics


Example 12.6 : Salim opened a savings bank account with a bank on 9th January 2002 with
a cash deposit of Rs 10000. Subsequently he deposited Rs 2000 on the 8th day of every month.
He withdrew Rs 3000 on 25th April and Rs 6000 on 28th June 2002. Write all entries of the
passbook.
If the bank pays interest at the rate of 4% per annum, calculate the interest upto the last day
of 30th June 2002 and make the entry in the passbook alongwith the balance.
Solution : The entries in the passbook are as below :

         Date          Particulars    Amount withdrawn            Amount Deposited         Balance

                                           Rs             P         Rs             P        Rs P

         2002

         9th Jan.    By cash                      —                   10000.00             10000.00

         8th Feb.    By Cash                      —                      2000.00           12000.00

         8th March By Cash                        —                      2000.00           14000.00

         8th April   By Cash                      —                      2000.00           16000.00

         25th April To Cash                     3000.00                    —               13000.00

         8th May     By Cash                      —                      2000.00           15000.00

         8th June    By Cash                      —                      2000.00           17000.00

         28th June To Cash                      6000.00                    —               11000.00

      Details of qualifying amount for the calculation of interest are :

        Month        January February       March         April       May          June       Total
        Amount       10000      12000       14000         13000      15000         11000     75000
        (in Rs)

                                                      75000 × 1 × 4
      ∴ Interest upto 30th June, 2002 = Rs                          = Rs 250
                                                        100 × 12

      The interest entry is made on 1–7–2002 as below :

          1.7.2002           By Interest              —             250.00             11250.00


                                     CHECK YOUR PROGRESS 12.1

  1. Krishna Murthy opened a savings bank account in State Bank of India on 7th July 2002.
     His pass book has the following entries :
Banking                                                                                    281



          Date             Particulars    Amount withdrawn Amount Deposited    Balance
                                            Rs        P       Rs     P         Rs P

          2002
          7th July        By cash                —               1100.00       1100.00
          11th July       By Cash                —                400.00       1500.00
          25th August     By Cash                —               1000.00       2500.00
          10th September By Cheque               —               1500.00       4000.00

     Calculate the principal for which he will earn interest for the months of July, August and
     September 2002, together.
  2. The entries in the savings bank account pass book of Kamlesh are as under:

          Date            Particulars    Amount withdrawn Amount Deposited    Balance
                                           Rs        P      Rs       P        Rs P

          2002

          1st January     B/F                   —                —            15000.00

          10th January    By Cash               —             5000.00         20000.00

          9th February    By Cheque             —             5000.00         25000.00

          9th March       By Cash               —             5000.00         30000.00

          11th April      By Cash               —             5000.00         35000.00

          25th June       By Cheque             —             5000.00         40000.00

     Calculate the interest at the end of June 2002 at 4% per annum.
  3. The entries in the passbook of a savings bank account holder who opened his account
     of 11th January 2002 are as follows :

          Date           Particulars     Amount withdrawn Amount Deposited Balance
                                           Rs        P      Rs       P     Rs P
          2002
          11th January   By cash                —              5000.00        5000.00
          11th Feb.      By Cheque              —              5000.00        10000.00
          9th March      By Cheque              —              5000.00        15000.00
          6th June       To Cheque            10000.00            —           5000.00
          10th June      By Cash                —              15000.00       20000.00
          26th June      To Cash              16000.00            —           4000.00
282                                                                                   Mathematics


      If the rate of interest is 4% per annum, find the interest earned if the account is closed
      on :
      (i) 30th June, 2002
      (ii) 3rd July, 2002.
  4. Madhu’s Savings Bank Account passbook has the following entries :
       Date            Particulars     Amount withdrawn Amount Deposited       Balance
                                         Rs        P      Rs       P            Rs P

       2002

       July 1          B/F                    —                 —              6000.00

       July 9          By Cheque              —               4000.00        10000.00

       Sept. 10        To Cheque            9000.00             —              1000.00

       Sept. 14        By Cash                —               4000.00          5000.00

       December 5      By Cash                —               4500.00          9500.00

       December 10     By Cash                —               1500.00        11000.00

       December 23     To Cheque           9000.00              —              2000.00

      If the rate of interest is 6% per annum, calculate the interest entry on 1st January 2003
      in the passbook alongwith the balance.
  5. A page from the pass book of savings bank account is given below :
      Date                   Particulars   Amount withdrawn Amount Deposited         Balance
                                             Rs        P      Rs       P             Rs P

      July 1, 2002           B/F                  —                  —                   2000.00

      July 11, 2002          By Cheque            —                8000.00            10000.00

      August 9, 2002         By Cheque            —               10000.00            20000.00

      November 25, 2002 To Cheque              15000.00              —                   5000.00

      December 19, 2000 By Cash                   —               15000.00            20000.00

      The account is closed on 2nd January 2003. Find the amount received if the rate of interest
      is 4% per annum.
  6. Kavita opens a savings bank account with a bank on 8th January, 2002 with a cash deposit
     of Rs 10000. Subsequently she deposited Rs 6000 on the 6th day of every month. She
     withdraws Rs 4000 on 3rd April and Rs 12000 on 10th June 2002. If the bank pays interest
     at the rate of 5% per annum, payable at the end of June and December, write all the entries,
     including interest, which are made upto 1st July 2002.
Banking                                                                                    283


12.4.3 Current Account
In a saving bank account, the account holder is allowed to have a limited number of withdrawals
in a half year. Big business concerns, companies, government organisations etc., have to do
a number of transactions every day. For them banks offer a different type of account called
current account. For this account, there is no limit on number of withdrawals or on the amount
of withdrawals but the banks do not pay interest. Rather, sometimes, they charge some money
as service charges. Here, the minimum balance for individuals account is Rs 5000 while for
big concerns, it is Rs 10000.
Depending upon the goodwill of the individual/company, banks allow the current account
holder to get money over and above their deposits called overdraft.

12.4.4 Fixed Deposit Account
Suppose you have some money which is not required for some time. The scheme suitable for
depositing such money is the Fixed Deposit or Term deposit. Here the depositor agrees to
keep the money with the bank for a fixed time. Obviously, the bank can use this money more
freely than the money kept in the savings bank account. Hence the banks offer higher rates
of interest on such deposits depending upon the period of deposits.
The rate of interest per annum on term deposits is as below :
 (i) For 46 days and above but less than 179 days.             5%
 (ii) For six months and above but less than 1 year.           6%
(iii) For one year and more.                                  6.5%
For senior citizens, and additional interest of 0.5% is given on deposits.
The total amount receivable after the expiry of the time is called maturity value.
Example 12.7 : Anju deposited Rs 2920 in a fixed deposit scheme in a bank for 60 days. If
the bank pays interest at 6% per annum, find the amount she receives at the end of 60 days.

                                                                 60
Solution : Here P = Rs 2920, R = 6% per annum and T =                year
                                                                 365

                                         FG 2920 × 6 × 60IJ
           ∴       Interest = PRT = Rs    H 100 × 365 K
                            = Rs 28.80
∴   Amount Received by Anju = Rs (2920 + 28.80)
                            = Rs 2948.80
Example 12.8 : Joginder makes a fixed deposit of Rs 31250 in a bank for 1½ years. If the
rate of interest is 8% per annum compounded half yearly, find the maturity value of the money
deposited by him.
284                                                                                  Mathematics


Solution : Note here that the interest for the first half year also forms a part of principal for
the second half year and likewise for the third half years well. Thus, we shall make use of
the formula for compound interest.
                            8
Here P = Rs. 31250, R =       = 4% per half year
                            2
            1
and T = 1     year = 3 Half years
            2
            ⇒            n = 3.

            ∴      Amount = P(1 + R)n = Rs 31250 1 +
                                                      4
                                                     100
                                                          FH         IK   3



                            = Rs 35152
Maturity value of the deposit = Rs 35152
Example 12.9 : Amit makes a fixed deposit of Rs 31250 in a bank for 1½ years. If the rate
of interest is 8% per annum compounded yearly, find the maturity value of the money deposited
by him.
                                           1
Solution : Here P = Rs 31250, R = 8%, T = 1 years.
                                           2

                                     FH
                                      8
Amount after one year = Rs 31250 1 + 100
                                               IK
                  1
and amount after 1 year
                  2

                                          FH8
                          A = Rs 31250 1 + 100
                                                    IK FH1 + 100IK
                                                              4

                            = Rs 31250 × 1.08 × 1.04 = Rs 35100
Hence, the maturity value = Rs 35100.
Note : Note the difference in the maturity value in Example 8 and Example 9. In example 8,
the interest is compounded half yearly while in Example 9, the interest is compounded yearly.
Example 12.10 : Kapil makes a fixed deposit of Rs 20000 in a bank in a year. If the rate of
interest 8% per annum compounded quarterly, find the maturity value of the money deposited
by him.
Solution : Here P = Rs. 20000, R = 2% per quarter, Time = 4 quarters

            ∴             A = P(1 + R)n = Rs 20000 1 +
                                                        2
                                                       100
                                                          FH         IK   4



                            = Rs 20000 × 1.02 × 1.02 × 1.02 × 1.02
                            = Rs 21648.64
 Hence the maturity value = Rs 21649 (approx.)
Banking                                                                                   285


Example 12.11 : How much money should Nirmal deposit in a fixed deposit account in a bank
so that she gets Rs 456976 after two years, the rate of interest being 8% per annum compounded
half yearly.

Solution : Here     P = ?, A = Rs 456976, R = 4% per half year and
                    T = 2 year = 4 half years i.e. n = 4
          We know that A = P(1 + R)n


           ∴                     FH
                   456976 = P 1 + 4
                                 100
                                            IK   4
                                                       FH IK
                                                     = P 26
                                                         25
                                                               4




                                      456976 × 25 × 25 × 25 × 25
                            P = Rs
                                          26 × 26 × 26 × 26
                             = Rs 390625
Hence amount to be deposited = Rs 390625.


                                      CHECK YOUR PROGRESS 12.2

  1. Find the amount at the end of 9 months if Rs 50000 is deposited and the interest 8% per
     annum is compounded quarterly.
  2. Charu makes a fixed deposit of Rs 8000 in a bank for 1½ years. It the rate of interest
     is 10% per annum and the interest is compounded half yearly, find the maturity value of
     the money deposited by her.
  3. Pankaj deposits Rs 75000 in a fixed deposit account for 3 years. If the rate of interest
     is 10% per annum compounded annually, find the maturity value of the money deposited
     by him.
  4. How much money should Shanta deposit in a fixed deposit account in a bank so as to
     enable her to receive a sum of Rs 9261 after 1½ years, the rate of interest being 10%
     per annum compounded half yearly ?
  5. How much money should Kamal deposit in a fixed deposit account in a bank so as to
     enable him to receive a sum of Rs 1061208 after nine months, the rate of interest being
     8% per annum compounded quarterly ?

LET US SUM UP
     There are different types of accounts in a bank. Some of these are :

     (i) Saving bank account

    (ii) Fixed or term deposit account

    (iii) Current account
286                                                                                    Mathematics


      In a saving bank account :

       (i) the bank pays interest for the month on the minimum closing balance from the 10th
           day of the month to the last day of the month.

      (ii) the interest is credited to the account every six months.

      Step for computing interest are :

       (i) Write down the minimum balance between the closing balance on 10th to the last
           day of the month.

      (ii) Add all the minimum balances for each month as per step (i) to obtain principal for
           one month.

      (iii) Calculate the simple interest on this sum for one month using the formula

                                           1
                     Interest = P × R ×
                                          12

           where P is Principal, R is rate of interest per annum and time 1 month i.e. 1/12 year.

      (iv) If account is opened after the 10th day of month, no interest is payable for that month.

      (v) No interest is paid for the month in which the account is closed.

                                    TERMINAL EXERCISE
  1. A page for the pass book of Mr. Dass’s Saving bank Account in a particular year is given
     below :


        Date          Particulars Amount withdrawn Amount Deposited              Balance
                                     Rs      P        Rs     P                    Rs P


        Jan. 9        By Cash                  —              15000.00         15000.00
        Feb. 10       By Cheque                —               8000.00         23000.00
        April 25      To Cheque           20000.00                —              3000.00
        June 7        By Cash                  —               2000.00           5000.00
        June 11       By Cash                  —              12000.00         17000.00


      If the rate of interest is 4% per annum, find the interest earned by Mr. Dass at the end
      of June on his savings bank account.
Banking                                                                                       287


  2. Sujata has a savings bank account in a bank. Her passbook has the following entries :

          Date         Particulars Amount withdrawn       Amount Deposited       Balance
                                     Rs        P             Rs     P            Rs P

          2002
          July 1       B.F.                —                      —              2500.00
          July 9       By Cheque           —                    2500.00          5000.00
          August 10    By Cash             —                    4000.00          9000.00
          October 19   To Cheque         6000.00                  —              3000.00
          November 2   By Cash             —                    9600.00        12600.00
          Dec. 20      To Cash           9200.00                  —              3400.00
          Dec. 27      By Cheque           —                   10600.00        14000.00

     The account is closed on 10th January, 2003. Find the amount received if the rate of interest
     is 4% per annum.
  3. Vandana makes a fixed deposit of Rs 62500 in a bank for 1½ years. If the rate of interest
     is 8% per annum compounded half yearly, find the maturity value of money deposited
     by her.

  4. Smith makes a fixed deposit of Rs 10000 in a bank for a year. If the rate of interest is
     8% per annum compounded quarterly, find the maturity value of the money deposited by
     her.

  5. How much money should Sarla deposit in a fixed deposit account in a bank so that she
     gets Rs 194481 after two years, the rate of interest being 10% per annum compounded
     half-yearly ?
288                                                                               Mathematics


                                         ANSWERS

Check Your Progress 12.1
 1. Rs 6600              2. Rs 583.33           3. (i) Rs 166.66         (ii) Rs 180
 4. Interest Rs 165, Balance Rs 2165            5. Rs 20240

 6. Date            Particulars           Debit             Credit              Balance
                                         Rs     P          Rs      P            Rs    P
      2002
      Jan. 5      By cash                   —                 10000.00           10000.00
      Feb. 6      By Cash                   —                  6000.00           16000.00
      March 6     By Cash                   —                  6000.00           22000.00
      April 3     To Cash                4000.00                —                18000.00
      April 6     By Cash                   —                  6000.00           24000.00
      May 6       By Cash                   —                  6000.00           30000.00
      June 6      By Cash                   —                  6000.00           36000.00
      June 10     To Cash                12000.00               —                24000.00
      July 1      By interest               —                   525.00           24525.00


Check Your Progress 12.2
 1. Rs 53060.40       2. Rs 9261        3. Rs 99825   4. Rs 8000          5. Rs 1000000

Terminal Exercise
 1. Rs 240            2. Rs 14140       3. Rs 70304   4. Rs 10824.32      5. Rs 160000

				
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